Hi Jarin,
Going by the CoC formula in the Wikipedia article, one should input the anticipated viewing distance and enlargement factor, in addition to your personally desired print resolution, specified in lp/mm (line pairs per millimeter).
Reading the post I've quoted, above, it looks as if you're letting the formula dictate your closest anticipated viewing distance - putting the cart before the proverbial horse. Adults with healthy vision can typically focus no more closely than 25 cm (about 10 inches). That's why 25 cm has long been the so-called "standard viewing distance" when discussing resolution in terms of lp/mm (vs. angular resolution, expressed in arc-minutes, where distance is irrelevant.)
THX, the people who provide specs for theaters, both commercial and home theaters, fit their viewing distance calculations to an assumed maximum human acuity of 1.0 arc-minute, which equates to 6.88 lp/mm at a viewing distance of 25cm. Double the viewing distance and you can go to 3.44 lp/mm, yet still deliver 1.0 arc-minute of angular resolution.
Many photographic texts, however, including John B. Williams'
Image Clarity: High Resolution Photography, consider 8 lp/mm to be the maximum resolution of healthy human vision at the standard viewing distance of 25cm. Of course, it varies from person to person, but I once read that eagles can resolve 24 lp/mm at 25cm, so I think it's safe to assume that most humans are limited to less than 10 lp/mm.
8 lp/mm at 25cm is equivalent to 0.86 arc-minute of angular resolution. I really suspect THX is rounding up from 0.86 to 1.0 arc-minute to make their theater calculations a little easier, but the net impact of that rounding, if indeed it was a conscious decision to round up to the nearest integer, is that they are telling people to sit a lot closer to their 1080p flatscreen TVs (and twice as close, still, to their 4k flatscreens) than they would if THX would acknowledge that we can resolve 0.86 arc-minute (8 lp/mm at 25cm) instead of only 1.0 arc-minute (6.88 lp/mm at 25cm).
Reading between the lines, it sounds as if you anticipate (or desire to support) a minimum viewing distance of 25cm (the closest distance at which healthy eyes can typically focus), a 4x enlargement factor and a desired print resolution of 5 lp/mm at 25cm.
Running the equation...
Max. permissible on-film CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25
CoC (mm) = 25 / 5 / 4 / 25 = 0.05 mm <--- Try this in your DoF calculations.
Note that if somebody views your print at a distance of 40 cm (15.75 inches) instead of 25 cm (9.84 inches), they will perceive a resolution equivalent to viewing an 8 lp/mm print at 25cm. It's only if they can focus more closely than 25cm and choose to do so, that they will perceive subject detail at something less than the equivalent of 5 lp/mm viewed at 25cm. And frankly, it's more likely that people will be looking at a 32x40-inch print from distances greater than 25cm. So... 5 lp/mm is probably "critical enough" for a 4x enlargement when your final print dimensions are that large.
Regarding your concern for the ratio of line pairs to CoCs, there are many references which say that a 0.2 mm CoC at the film or sensor equates to 5 lp/mm prior to enlargement. There are several texts that say CoC, prior to enlargement, is the reciprocal of the lp/mm you will record on film or at the sensor, or lp/mm is the reciprocal of the maximum CoC diameter you permit via DoF calculations and adherence to those calculations.
If, for example, you anticipate an 8x enlargement to produce 8x12-inch prints from a 35mm negative, 5 lp/mm at the print requires 40 lp/mm at the negative and thus, you must perform your DoF calculations with a maximum permissible in-camera CoC diameter of 1/40 = 0.025mm. The reciprocal of 40 lp/mm is roughly 0.03 mm. Sound familiar? Many people are disappointed with DoF calculators that use 0.03mm CoCs for 35mm format. They need to increase their desired print resolution from 5 lp/mm to 8 lp/mm, for example, and do the DoF calculations to limit on-film CoC diameters to the reciprocal of 8 lp/mm or 0.125 mm (but it's really tough to achieve 64 lp/mm on-film to deliver 8 lp/mm in an 8x enlargement, except with the likes of Tech Pan and some very good glass.
One last tip: Once you've calculated the maximum permissible CoC diameter for a specified viewing distance, enlargement factor and desired print resolution in lp/mm, you can calculate the
f-Number at which diffraction will just begin to inhibit your desired print resolution as follows:
Max f-Number = CoC / 0.00135383
Warning: This formula only works if you've used the Wikipedia CoC equation (above) that takes into account your desired print resolution, viewing distance, and enlargement factor.
Thus, for an in-camera CoC diameter of 0.05 mm, you can stop down to 0.05 / 0.00135383 = 36.9, or about
f/32 + 1/3 stop without concern for diffraction inhibiting your print resolution goal of 5 lp/mm in a 4x enlargement to be viewed at 25cm.
How was that constant 0.0013583 derived? Search for it on this page:
http://www.faqs.org/faqs/rec-photo/lenses/tutorial/
OK, I'm rambling, but I hope that helps.
Mike